arXiv subjects

Boris Belousov

Publications and source records attributed to Boris Belousov.

29 records · Page 2Linked to original sources

arXiv2021

Distributionally Robust Trajectory Optimization Under Uncertain Dynamics via Relative Entropy Trust-Regions

Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid control. State-of-the-art algorithms have focused on data-driven approaches that infer the system dynamics online and incorporate posterior uncertainty during planning and control. Despite their success, such approaches are still susceptible to catastrophic errors that may arise due to statistical learning biases, unmodeled disturbances, or even directed adversarial attacks. In this paper, we tackle the problem of dynamics mismatch and propose a distributionally robust optimal control formulation that alternates between two relative entropy trust-region optimization problems. Our method finds the worst-case maximum entropy Gaussian posterior over the dynamics parameters and the corresponding robust policy. Furthermore, we show that our approach admits a closed-form backward-pass for a certain class of systems. Finally, we demonstrate the resulting robustness on linear and nonlinear numerical examples.

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arXiv2021

Continuous-Time Fitted Value Iteration for Robust Policies

Solving the Hamilton-Jacobi-Bellman equation is important in many domains including control, robotics and economics. Especially for continuous control, solving this differential equation and its extension the Hamilton-Jacobi-Isaacs equation, is important as it yields the optimal policy that achieves the maximum reward on a give task. In the case of the Hamilton-Jacobi-Isaacs equation, which includes an adversary controlling the environment and minimizing the reward, the obtained policy is also robust to perturbations of the dynamics. In this paper we propose continuous fitted value iteration (cFVI) and robust fitted value iteration (rFVI). These algorithms leverage the non-linear control-affine dynamics and separable state and action reward of many continuous control problems to derive the optimal policy and optimal adversary in closed form. This analytic expression simplifies the differential equations and enables us to solve for the optimal value function using value iteration for continuous actions and states as well as the adversarial case. Notably, the resulting algorithms do not require discretization of states or actions. We apply the resulting algorithms to the Furuta pendulum and cartpole. We show that both algorithms obtain the optimal policy. The robustness Sim2Real experiments on the physical systems show that the policies successfully achieve the task in the real-world. When changing the masses of the pendulum, we observe that robust value iteration is more robust compared to deep reinforcement learning algorithm and the non-robust version of the algorithm. Videos of the experiments are shown at https://sites.google.com/view/rfvi

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arXiv2021

A Probabilistic Interpretation of Self-Paced Learning with Applications to Reinforcement Learning

Across machine learning, the use of curricula has shown strong empirical potential to improve learning from data by avoiding local optima of training objectives. For reinforcement learning (RL), curricula are especially interesting, as the underlying optimization has a strong tendency to get stuck in local optima due to the exploration-exploitation trade-off. Recently, a number of approaches for an automatic generation of curricula for RL have been shown to increase performance while requiring less expert knowledge compared to manually designed curricula. However, these approaches are seldomly investigated from a theoretical perspective, preventing a deeper understanding of their mechanics. In this paper, we present an approach for automated curriculum generation in RL with a clear theoretical underpinning. More precisely, we formalize the well-known self-paced learning paradigm as inducing a distribution over training tasks, which trades off between task complexity and the objective to match a desired task distribution. Experiments show that training on this induced distribution helps to avoid poor local optima across RL algorithms in different tasks with uninformative rewards and challenging exploration requirements.

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arXiv2020

Underactuated Waypoint Trajectory Optimization for Light Painting Photography

Despite their abundance in robotics and nature, underactuated systems remain a challenge for control engineering. Trajectory optimization provides a generally applicable solution, however its efficiency strongly depends on the skill of the engineer to frame the problem in an optimizer-friendly way. This paper proposes a procedure that automates such problem reformulation for a class of tasks in which the desired trajectory is specified by a sequence of waypoints. The approach is based on introducing auxiliary optimization variables that represent waypoint activations. To validate the proposed method, a letter drawing task is set up where shapes traced by the tip of a rotary inverted pendulum are visualized using long exposure photography.

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arXiv2019

HJB Optimal Feedback Control with Deep Differential Value Functions and Action Constraints

Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory from a specific starting configuration. In this paper we propose deep optimal feedback control to learn an optimal feedback policy rather than a single trajectory. By exploiting the inherent structure of the robot dynamics and strictly convex action cost, we can derive principled cost functions such that the optimal policy naturally obeys the action limits, is globally optimal and stable on the training domain given the optimal value function. The corresponding optimal value function is learned end-to-end by embedding a deep differential network in the Hamilton-Jacobi-Bellmann differential equation and minimizing the error of this equality while simultaneously decreasing the discounting from short- to far-sighted to enable the learning. Our proposed approach enables us to learn an optimal feedback control law in continuous time, that in contrast to existing approaches generates an optimal trajectory from any point in state-space without the need of replanning. The resulting approach is evaluated on non-linear systems and achieves optimal feedback control, where standard optimal control methods require frequent replanning.

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arXiv2019

Receding Horizon Curiosity

Sample-efficient exploration is crucial not only for discovering rewarding experiences but also for adapting to environment changes in a task-agnostic fashion. A principled treatment of the problem of optimal input synthesis for system identification is provided within the framework of sequential Bayesian experimental design. In this paper, we present an effective trajectory-optimization-based approximate solution of this otherwise intractable problem that models optimal exploration in an unknown Markov decision process (MDP). By interleaving episodic exploration with Bayesian nonlinear system identification, our algorithm takes advantage of the inductive bias to explore in a directed manner, without assuming prior knowledge of the MDP. Empirical evaluations indicate a clear advantage of the proposed algorithm in terms of the rate of convergence and the final model fidelity when compared to intrinsic-motivation-based algorithms employing exploration bonuses such as prediction error and information gain. Moreover, our method maintains a computational advantage over a recent model-based active exploration (MAX) algorithm, by focusing on the information gain along trajectories instead of seeking a global exploration policy. A reference implementation of our algorithm and the conducted experiments is publicly available.

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arXiv2019

Self-Paced Contextual Reinforcement Learning

Generalization and adaptation of learned skills to novel situations is a core requirement for intelligent autonomous robots. Although contextual reinforcement learning provides a principled framework for learning and generalization of behaviors across related tasks, it generally relies on uninformed sampling of environments from an unknown, uncontrolled context distribution, thus missing the benefits of structured, sequential learning. We introduce a novel relative entropy reinforcement learning algorithm that gives the agent the freedom to control the intermediate task distribution, allowing for its gradual progression towards the target context distribution. Empirical evaluation shows that the proposed curriculum learning scheme drastically improves sample efficiency and enables learning in scenarios with both broad and sharp target context distributions in which classical approaches perform sub-optimally.

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arXiv2019

Building a Library of Tactile Skills Based on FingerVision

Camera-based tactile sensors are emerging as a promising inexpensive solution for tactile-enhanced manipulation tasks. A recently introduced FingerVision sensor was shown capable of generating reliable signals for force estimation, object pose estimation, and slip detection. In this paper, we build upon the FingerVision design, improving already existing control algorithms, and, more importantly, expanding its range of applicability to more challenging tasks by utilizing raw skin deformation data for control. In contrast to previous approaches that rely on the average deformation of the whole sensor surface, we directly employ local deviations of each spherical marker immersed in the silicone body of the sensor for feedback control and as input to learning tasks. We show that with such input, substances of varying texture and viscosity can be distinguished on the basis of tactile sensations evoked while stirring them. As another application, we learn a mapping between skin deformation and force applied to an object. To demonstrate the full range of capabilities of the proposed controllers, we deploy them in a challenging architectural assembly task that involves inserting a load-bearing element underneath a bendable plate at the point of maximum load.

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arXiv2019

Entropic Risk Measure in Policy Search

With the increasing pace of automation, modern robotic systems need to act in stochastic, non-stationary, partially observable environments. A range of algorithms for finding parameterized policies that optimize for long-term average performance have been proposed in the past. However, the majority of the proposed approaches does not explicitly take into account the variability of the performance metric, which may lead to finding policies that although performing well on average, can perform spectacularly bad in a particular run or over a period of time. To address this shortcoming, we study an approach to policy optimization that explicitly takes into account higher order statistics of the reward function. In this paper, we extend policy gradient methods to include the entropic risk measure in the objective function and evaluate their performance in simulation experiments and on a real-robot task of learning a hitting motion in robot badminton.

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arXiv2019

Entropic Regularization of Markov Decision Processes

An optimal feedback controller for a given Markov decision process (MDP) can in principle be synthesized by value or policy iteration. However, if the system dynamics and the reward function are unknown, a learning agent must discover an optimal controller via direct interaction with the environment. Such interactive data gathering commonly leads to divergence towards dangerous or uninformative regions of the state space unless additional regularization measures are taken. Prior works proposed bounding the information loss measured by the Kullback-Leibler (KL) divergence at every policy improvement step to eliminate instability in the learning dynamics. In this paper, we consider a broader family of $f$-divergences, and more concretely $α$-divergences, which inherit the beneficial property of providing the policy improvement step in closed form at the same time yielding a corresponding dual objective for policy evaluation. Such entropic proximal policy optimization view gives a unified perspective on compatible actor-critic architectures. In particular, common least-squares value function estimation coupled with advantage-weighted maximum likelihood policy improvement is shown to correspond to the Pearson $χ^2$-divergence penalty. Other actor-critic pairs arise for various choices of the penalty-generating function $f$. On a concrete instantiation of our framework with the $α$-divergence, we carry out asymptotic analysis of the solutions for different values of $α$ and demonstrate the effects of the divergence function choice on common standard reinforcement learning problems.

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arXiv2018

f-Divergence constrained policy improvement

To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined by the Kullback-Leibler (KL) divergence, which not only captures the notion of distance well but also yields closed-form solutions. In this paper, we consider a more general class of f-divergences and derive the corresponding policy update rules. The generic solution is expressed through the derivative of the convex conjugate function to f and includes the KL solution as a special case. Within the class of f-divergences, we further focus on a one-parameter family of $α$-divergences to study effects of the choice of divergence on policy improvement. Previously known as well as new policy updates emerge for different values of $α$. We show that every type of policy update comes with a compatible policy evaluation resulting from the chosen f-divergence. Interestingly, the mean-squared Bellman error minimization is closely related to policy evaluation with the Pearson $χ^2$-divergence penalty, while the KL divergence results in the soft-max policy update and a log-sum-exp critic. We carry out asymptotic analysis of the solutions for different values of $α$ and demonstrate the effects of using different divergence functions on a multi-armed bandit problem and on common standard reinforcement learning problems.

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